shiv and melee prioritization
I've had multiple encounters in which I went in for a shiv only to open a box and get shived myself, or went for a special execution or went in for a teammate pickup and ended up dying. People now seem to exploit this a lot. As with melee it auto locks on a downed player even though there's one punching you right next to it.
Solve the shiv thing by making shivs just a triangle tap and revives, special executions and supply box grabs a triangle hold (1s).
Make it that melee locks on to someone who's still up first!
One of the few improvements I feel this game should implement is button customization beyond the L1/R1 or L2/R2 buttons. A great option might be to use the aforementioned buttons you opt not to employ.
How many times have you gone to revive a player only to end up curb stomping the enemy your teammate just downed that was crawling next to them? It makes you feel like a prick... and if their is no open mic communication your teammate may feel that is precisely what you are (and that animosity can be costly later on as they let you bleed out at their feet).
Another shiv issue (slightly off topic here) that many of us have encountered is the failure of the shiv option pop-up to even become available.
Ultimately I think all these concerns could be eliminated through broader controller mapping options.